At time of writing, Wine's default Windows mode is XP. Make sure you set the correct Windows mode in winecfg or the installer will simply refuse to continue.
You can use an extraction tool, such as file-roller, to extract the .cab from the .exe, and then extract all the files from that into a folder.
Remember: Test results can not be accepted for this method as "installing is an important part of testing".
This note was originally added to IE Version 5, but may be relevant to all versions.
Don't run IE on an RW mounted DOS partition !
Pretty problematic directory renaming/corruption can happen.
This seems to happen if Wine doesn't have access to certain Windows registry keys.
Renames e.g. "Program Files" to "$!$!$!$!.pfr" and does other horrible things.
BTW, it does not only happen with IE, as it seems to be a generic Windows
Setup process of Explorer which is doing this, which can be launched
under multiple circumstances.
To be safe, use a backup copy only, i.e. copy all relevant windows files over
e.g. to an ext2 partition.